Scelta multipla
What is the root-mean-square speed of a carbon monoxide molecule at 27°C?
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7. Gases
Root Mean Square Speed
Scelta multipla
At 25 °C, which of the following gases has molecules with the greatest average molecular speed?
A
He
B
N2
C
O2
D
CO2
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Recall that the average molecular speed of a gas molecule is related to its molar mass and temperature by the root-mean-square speed formula:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where \(v_{rms}\) is the root-mean-square speed, \(R\) is the gas constant, \(T\) is the temperature in Kelvin, and \(M\) is the molar mass in kilograms per mole.
Note that the temperature \(T\) is the same for all gases given (25 °C, which is 298 K), so the variable that affects the average molecular speed is the molar mass \(M\) of each gas.
List the molar masses of the gases:
- Helium (He): approximately 4 g/mol
- Nitrogen (N\_2): approximately 28 g/mol
- Oxygen (O\_2): approximately 32 g/mol
- Carbon dioxide (CO\_2): approximately 44 g/mol
Since \(v_{rms}\) is inversely proportional to the square root of the molar mass, the gas with the smallest molar mass will have the greatest average molecular speed.
Compare the molar masses and conclude that helium, having the smallest molar mass, will have the greatest average molecular speed at 25 °C.
